How to calculate the Delta-v to counteract the athmosferic drag

[sirmatthew]

The question is simple: i want to do some math to get the required Delta-v to get a Low orbit on Kerbin. The problem is that i have to calculate not only the basic Delta-v to lift-off, and the delta-v to win gravitational drag, but also the delta-v required to win the athmosferic drag. How can I do it?

(and obviously i don't want to look at a delta-v map...)

Edited July 14, 2014 by sirmatthew

[xcorps]

Here you, found it with a search.

// Delta V to reach orbit around a body with no atmosphere, from sea level, r1 is the equatorial radius

public static double getToOrbit(double gravParameter, double r1, double orbitHeight, double siderealRotationVelocity) {

double r2 = r1 + orbitHeight;

return Math.sqrt(gravParameter / r1) * Math.sqrt((2 * r2) / (r1 + r2))

+ (Math.sqrt(gravParameter / r2) * (1 - (Math.sqrt((2 * r1) / (r1 + r2))))) - siderealRotationVelocity;

}

// Additional Delta V to reach orbit around a body with an atmosphere

public static double getToOrbitAtmo(double surfaceGravity, double scaleHeight, double terminalVelocity) {

return (4 * surfaceGravity * scaleHeight) / terminalVelocity;

}

// Get terminal velocity at a specific altitude.

public static double getTerminalVelocity(double surfacePressure, double altitude, double scaleHeight, double planetMass, double equatorialRadius) {

double G = 6.67e-11; // Gravitational constant

double r = equatorialRadius + altitude;

double atmosphericDensity = 1.2230948554874 * surfacePressure * Math.exp(-altitude / scaleHeight);

return Math.sqrt((1250 * G * planetMass) / (r * r * atmosphericDensity));

}

For Kerbin:

Double toOrbit4 = (getToOrbit(3.5316000e12, 600000, 69078 + mClearanceValue, 174.53) + getToOrbitAtmo(9.81, 5000, 100.2));

For a 69,079m orbit, the absolute minimum possible with a flawless ascent, this returns just over 4,338.2 dV

For a 100km orbit, mClearanceValue = 30922, so with a perfect ascent, to a circular 100km orbit, this returns: 4389.4 dV

[UmbralRaptor]

Any idea where Amagi82 got the values for drag?

[xcorps]

http://wiki.kerbalspaceprogram.com/wiki/Atmosphere

[UmbralRaptor]

http://wiki.kerbalspaceprogram.com/wiki/Atmosphere

That page doesn't seem to cover the (4 * surfaceGravity * scaleHeight) / terminalVelocity, though.

Maybe if I try integrating the drag over a distance with some sketchy path length assumptions...?

[sirmatthew]

ok thank you!

[Mr Shifty]

That page doesn't seem to cover the (4 * surfaceGravity * scaleHeight) / terminalVelocity, though.

Maybe if I try integrating the drag over a distance with some sketchy path length assumptions...?

K^2 posted his quick and dirty derivation about a year ago here (and further on in the same thread.)

[UmbralRaptor]

K^2 posted his quick and dirty derivation about a year ago here (and further on in the same thread.)

Excellent, thank you.